llowing is a portion of the regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal.
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Following is a portion of the regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal.
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?The Update to the Task Force Report on Blood Pressure Control in Children [12] reported the observed 90th per-centile of SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of average height are given in Table 11.18. Suppose we seek a more efficient way to display the data and choose linear regression to accomplish this task. age sbp 1 99 2 102 3 105 4 107 5 108 6 110 7 111 8 112 9 114 10 115 11 117 12 120 13 122 14 125 15 127 16 130 17 132 Do you think the linear regression provides a good fit to the data? Why or why not? Use residual analysis to justify your answer. Am I supposed to run a residual plot and QQ-plot for this question?
- The following output comes from regression using the actual HW9 scores and the Final test scores from intro stats one semester. Sample size: 50R (correlation coefficient) = 0.3658R-sq = 0.1338Estimate of error standard deviation: 10.36256Parameter estimates: Parameter Estimate Std. Err. DF T-Stat P-Value Intercept 43.558118 11.1716 48 3.899 0.0003 Slope 0.360048 0.132225 48 2.723 0.009 Assume no assumptions are violated. Form a 87% Confidence interval for how much your final is supposed to increase for each problem done on homework 9.Use 5 decimal placesThe accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter The predicted y-hat value for a diameter of 201 is 864. if we observed a weld that had a diameter of 235 that had a strength 1000, what would be its residual?The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenueas a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly GrossRevenue($1000s) Television Advertising($1000s) Newspaper Advertising($1000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 a. Develop an estimated regression equation with the amount of televisionadvertising as the independent variable.b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. c. Is the estimated regression equation coefficient for television advertisingexpenditures the same in part (a) and in part (b)? Interpret the coefficient in each case. d. Predict weekly gross revenue for a week when $3500 is spent on television advertising and $1800 is spent on newspaper advertising.
- A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…If a scatterplot is created in excel, and a line of regression is fit along with a derived functional form, what does it mean to describe and interpret them? What conclusions would be made about relationships between two recorded variables?The accompanying table lists systolic blood pressures (mm Hg) and diastolic blood pressures (mm Hg) of adult females. Find the prediction interval for a systolic blood pressure of 121mm Hg using a 99% confidence level. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. Systolic Diastolic 125 69 104 65 129 75 108 65 157 74 95 53 155 89 110 69 120 69 115 73 101 59 127 67 The 99% prediction interval for a systolic blood pressure of 121mm Hg is ____mm Hg<y<___mm Hg.
- Which of the following is not a plot of residuals typically used in multiple regression analysis?Select one:a. None of these b. Residuals versus correlation coefficients..c. Residuals versus X1.d. Residuals versus timee. Residuals versus X2.table 7 autocorrelations of the residuals from estimating the regression ΔgPMt = 0.0006 − 0.33301 ΔgPMt −1 + εt 1Q:1992–4Q:2001 (40 Observations) regression Statistics R-squared Standard error Observations Durbin–watson intercept ΔgPMt −1 ΔgPMt −4 Coefficient −0.0001 −0.0608 0.8720 0.9155 0.0057 40 2.6464 Standard error 0.0009 0.0687 0.0678 t-Statistic −0.0610 −0.8850 12.8683 lag 1 2 3 4 5 autocorrelation −0.1106 −0.5981 −0.1525 0.8496 −0.1099 table 8 shows the output from a regression on changes in the gPM for home Depot, where we have changed the specification of the ar regression. table 8 Change in gross Profit Margin for home Depot 1Q:1992–4Q:2001 a. identify the change that was made to the regression model. b. Discuss the rationale for changing the regression specificationA sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employee. A sample of 10 employees was chosen, and the following data were collected. A. Is the estimated regression equation appropriate and adequate